Weighted universal Value-at-Risk Superadditivity for discrete distributions

2026-09-22

AI Summary

研究解决了关于离散分布中加权通用风险值超可加性几乎不成立的问题，证明了对于无限均值的离散分布，独立同分布随机变量的凸组合不能在随机上优于母体分布。

Abstract

The concept of weighted universal Value-at-Risk superadditivity (WUVS) was recently introduced by Chen et al. (2026) as a generalization of the question whether for some infinite mean distributions convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. In this short note we prove that the property WUVS can basically never hold for discrete distributions except for the case of comonotonicity. This implies as a corollary that for discrete distributions with infinite mean it can also never hold that convex combinations of i.i.d. random variables can stochastically dominate the parent distribution. This settles an open problem mentioned in M\"uller (2025).

Problem

• WUVS
• discrete distributions
• infinite mean
• stochastic dominance

Innovation

• Weighted universal Value-at-Risk superadditivity
• discrete distributions
• comonotonicity
• infinite mean